Intractable argument depends on mathematically difficult propositions such as one-way functions, digital signature algorithms, or encryption algorithms. Such argument can rely on the existence of tamper-resistant hardware within the system for their implementation design.

Infeasible argument depends on mathematically infeasible propositions such as solving a system of equations with more variables than equations. An example may be the use of mathematical objects such as Shamir's secret sharing schemes. Such argument can rely on the existence of tamper-resistant hardware within the systems for their implementation design -- such systems may require the use of more than one secret to construct or reconstruct a capability with an automatically implied designation that the system can understand.

Examples

Some examples of unforgeable capabilities:

Designations of objects in the E language. Those who hold these capabilities have the permission to invoke any method supported by the designated object.

Designations of functions and procedures in Emily. Those who hold these capabilities have the permission to call designated functions or procedures.

Some examples of capabilities that are infeasible to forge:

Designations of remote objects in E, such as captp://*orwqphzlugjwqj2wozz7tmg47ime466j@74.125.87.147:55189/oa6vn5whhapylswhzesdlqh5ppmjkcrq. Those who hold these capabilities have the permission to invoke any method supported by the designated object.